In this paper, the author aims to explore some of the cognitive processes involved in simultaneous interpreting. The author’s starting point is a consideration of what is involved in participating (as conversionalist or discussant) in multi-source spoken discourse, in which meanings are publicly negotiated through successive turns-at-talk. It is argued that the interpreter as mediator does not in principle have a part to play in this process of negotiation, such that more space is available in working memory for the cognitive processes peculiar to interpreting.